{% extends 'homepage.html' %}
{% block content %}

{% if not error %}

<h2>Galois orbit</h2>
<h4>Weight: {{ weight }}&nbsp;&nbsp;&nbsp;&nbsp;
  
  {% if form %}
  [{{ form }}]
  {% else %}
  [Need to indicate Maass, Interesting, etc. here]
  {% endif %}
  
</h4>

<h2>Number field containing all coefficients</h2>
<div class="box1"><div class="small">{{ the_form[0] }}</div></div>

<h2>As polynomial in <a class="knowl-title" knowl="{{ generators }}">generators</a></h2>
{% if the_form[1] %} 
<div class="box1"><div class="small">{{ the_form[1] }}</div></div>
{% else %}
<div class="box1"><div class="small">Not applicable</div></div>
{% endif %}

<h2>Hecke eigenvalues
  <button name="Eigenvalues" value="Download" onclick="window.location.href = '{{ the_form[5] }}'">Download</button>
</h2>
  <form action="/ModularForm/GSp/Q" method="get">
    <input type="hidden" name="group" value="{{ group }}" />
    <input type="hidden" name="page" value="specimen" /> 
    <input type="hidden" name="form" value="{{ form_name }}" /> 
    <input type="hidden" name="weight" value="{{ weight }}" /> 
    <label>The eigenvalues are shown reduced modulo</label>
    <input type="text" name="ev_modulus" value="{{ ev_modulus }}" size=10 maxlength=10/>
    <span class="formexample">e.g. 17 (0 means no reduction)</span>
    <button type="submit" value="reduce"> Reduce again</button>
  </form>
<div class="box1">
<div class="small">
  <table>
    <thead>
      <tr><th>n</th><th>&lambda;(n)</th></tr>
    </thead>
    {% for l,val in the_form[2] %}
    <tr class = "{{ loop.cycle( 'odd', 'even') }}"><td>{{ l }}</td><td>{{ val }}</td></tr>
    {% endfor %}
  </table>
</div></div>

<h2>Fourier coefficients
  <button name="Fourier coefficients" value="Download" onclick="window.location.href = '{{ the_form[4] }}'">Download</button>
</h2>
{% if 'Sp8Z' == group %}
{% set form_index = '\(T=(m_{11}, m_{22}, \dots, m_{34})\)' %}
<p>
  In this table a tuple \((m_{11}, m_{22}, m_{33}, m_{44}, m_{12}, m_{13}, m_{23}, m_{14}, m_{24}, m_{34})\ \) stands for the quadratic form
  \(T = \begin{bmatrix}
  m_{11} & m_{12} & m_{13} & m_{14}
  \\
  m_{21} & m_{22} & m_{23} & m_{24}
  \\
  m_{31} & m_{32} & m_{33} & m_{34}
  \\
  m_{41} & m_{42}& m_{43}& m_{44}
  \end{bmatrix}\)
  of discriminant \(D = {\rm det}(T)\).
  The Fourier expansion of the modular form is given as
  \[
  f(Z)=\sum_{T}a(T)\;e^{2\pi i\big(({\rm trace}(TZ)\big)}.
  \]
  {% if form_name != 'Ikeda' %}
  Coefficients for only very few forms are known. The table lists only the known ones. In particular, it is by no means complete for a
  given discriminant \(D\).
  {% endif %}
{% elif 'Sp6Z' == group %}
  {% set form_index = '\(T=(a, b, c, d, e, f)\)' %}
  <p>
  In this table a tuple \((a, b, c, d, e, f)\ \) stands for the quadratic form
  \(T = \begin{bmatrix}
  2a & d  & e
  \\
  d  & 2b & f
  \\
  e  & f  & 2c
  \end{bmatrix}\)
  of discriminant \(D = {\rm det}(T)\).
  The Fourier expansion of the modular form is given as
  \[
  f(Z)=\sum_{T}a(T)\;e^{2\pi i\big(({\rm trace}(TZ)\big)}.
  \]
{% else %}
  {% set form_index = '\(T=(n,r,m)\)' %}
  <p>
    In this table a triple \((n,r,m)\) stands for the quadratic form \(\begin{bmatrix}n&r/2\\r/2&m\end{bmatrix}\) of discriminant \(D = r^2-4nm\).
    The Fourier expansion of the modular form is given as
    \[
    f(\tau,z,\tau')=\sum_{T=(n,r,m)}a(T)\;e^{2\pi i(n\tau+rz+m\tau')}.
    \]
{% endif %}
  <form action="/ModularForm/GSp/Q" method="get">
    <input type="hidden" name="group" value="{{ group }}" />
    <input type="hidden" name="page" value="specimen" /> 
    <input type="hidden" name="form" value="{{ form_name }}" /> 
    <input type="hidden" name="weight" value="{{ weight }}" /> 
    <label>The coefficients are shown reduced modulo</label>
    <input type="text" name="fc_modulus" value="{{ fc_modulus }}" size=5 maxlength=5/>
    <span class="formexample">e.g. 17 (0 means no reduction)</span>
    <button type="submit" value="reduce"> Reduce again</button>
  </form>
</p>
<div class="box1">
<div class="small">
  <table>
    <thead>
      <tr><th>\(|D|\)</th><th>{{ form_index }}</th><th>\(a(T)\)</th></tr>
    </thead>
    {% for l,val,disc in the_form[3] %}
    <tr class = "{{ loop.cycle( 'odd', 'even') }}"><td>{{ disc }}</td><td nowrap=''>{{ l }}</td><td>{{ val }}</td></tr>
    {% endfor %}
  </table>
</div></div>

{% else %}
{% include 'ModularForm_GSp4_Q/None.html' %}
{% endif %}

{% endblock %}

